Monotone comparative statics in ordered vector spaces

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing results on increasing differences and supermodularity for C-1 or C-2 functions. None of the results are based on the assumption that the order is Euclidean. As applications we consider a teamwork game and a monopoly union model.